What is chaotic behavior and how it is achieved in non-linear regression and artificial networks?
It looks like you have some common misconceptions about AI and neural networks.

First, AI programs generally do not try to imitate the human behaviour of a human brain. Instead, they try to imitate some higher-level behaviour. For example, they might imitate the reasoning process that you go through when you make a plan. In this context, the building-blocks (silicon or flesh) don't matter too much.

Second, artificial neural networks are also (mostly) not intended to imitate the human brain. Although they are inspired by the arrangement of neurons in a human brain, the networks used in most ANN systems have very little to do with real brains. The main similarity is that both systems have a lot of simple little computational units connected in patterns such that signals passed from one to another lead to interesting computations. However, real neurons produce lots of different kinds of signals, are connected in arbitrary ways, and randomization and transmission times play a significant role. Artificial neurons generally are deterministic, produce only one kind of signal (or sometimes a couple different kinds), are connected in extremely regular ways, and usually simulate instantaneous transmissions between neurons.